Interval Sheffer Stroke Basic Algebras and Yang-Baxter Equation

Author:

Oner Tahsin1,Katican Tugce1

Affiliation:

1. Department of Mathematics, Science Faculty , Ege University , Bornova , Izmir - Turkey

Abstract

Abstract In this study, we give basic definitions and notions about Sheffer stroke operation and Sheffer stroke basic algebra. After presenting Sheffer stroke basic algebra on a given interval, named interval Sheffer stroke basic algebra, we give some features of an interval Sheffer stroke basic algebra. Then we investigate solutions to the set-theoretical Yang-Baxter equation in this algebraic structure by using its features.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science

Reference22 articles.

1. Abbott, J. C. (1967), Implicational algebras, Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie, 11(1):3–23.

2. Baxter, R. J. (1972), Partition Function of the Eight-Vertex Lattice Model, Ann. Phys., 70: 193–228.

3. Baxter, R. J. (1982), Exactly Solved Models in Statical Mechanics, Academy Press, London, UK.

4. Chajda, I. (2015), Basic algebras, logics, trends and applications, Asian-European Journal of Mathematics, 8(03): 1550040.

5. Chajda, I. (2005), Sheffer operation in ortholattices, Acta Universitatis Palackianae Olomucensis, Facultas Rerum Naturalium, Mathematica, 44(1):19–23.

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